A Strict Comparison Principle for Integro-Differential Hamilton-Jacobi-Bellman Equations on Domains with Boundary
Analysis of PDEs
2025-12-04 v1 Probability
Abstract
This work provides a comparison principle for viscosity solutions to boundary value problems on (partially) bounded, cylindrical spaces. The comparison principle is based on a test function framework, that allows for the simultaneous treatment of diffusive as well as jump terms. Estimates in the proof of the comparison principle incorporate the use of Lyapunov functions that act as growth bounds for the solutions, effectively yielding a theory for unbounded viscosity solutions. We apply the results to a wide class of parabolic equations and elliptic problems on a space with corners.
Keywords
Cite
@article{arxiv.2512.04005,
title = {A Strict Comparison Principle for Integro-Differential Hamilton-Jacobi-Bellman Equations on Domains with Boundary},
author = {Serena Della Corte and Fabian Fuchs and Richard C. Kraaij and Max Nendel},
journal= {arXiv preprint arXiv:2512.04005},
year = {2025}
}